Our aim is to determine the asymptotic behaviour of a \({q}\) -Boltzmann random planar map \(M_{n,K_n}\)  conditioned to have \(n-1\)  edges and \(K_{n}+1\)  vertices, sampled from \(\mathbb {P}^{{q}}_{n,K_n}\) , and more precisely of the metric measured space obtained by endowing the set of vertices \(V(M_{n,K_n})\)  with the graph distance \(d_{\mathrm {gr}}\) , suitably rescaled, and the uniform probability measure \(p_{\mathrm {unif}}\) , in the Gromov–Hausdorff–Prokhorov topology (see e.g. [1]} for details on this topology).
